Photophysical Properties in C60 and Higher Fullerenes

The optical excitations in C$_{60}$ and higher fullerenes, including isomers of C$_{76}$, C$_{78}$, and C$_{84}$, are theoretically investigated. We use a tight binding model with long-range Coulomb interactions, treated by the Hartree-Fock and configuration-interaction methods. We find that the optical excitations in the energy region smaller than about 4 eV have most of their amplitudes at the pentagons. The oscillator strengths of projected absorption almost accord with those of the total absorption. Next, off-resonant third order susceptibilities are investigated. We find that third order susceptibilities of higher fullerenes are a few times larger than those of C$_{60}$. The magnitude of nonlinearity increases as the optical gap decreases in higher fullerenes. The nonlinearity is nearly proportional to the fourth power of the carbon number when the onsite Coulomb repulsion is $2t$ or $4t$, $t$ being the nearest neighbor hopping integral. This result, indicating important roles of Coulomb interactions, agrees with quantum chemical calculations of higher fullerenes.